Spaceplates are novel flatoptic devices that implement the optical response of a freespace volume over a smaller length, effectively “compressing space” for light propagation. Together with flat lenses such as metalenses or diffractive lenses, spaceplates have the potential to enable the miniaturization of any freespace optical system. While the fundamental and practical bounds on the performance metrics of flat lenses have been well studied in recent years, a similar understanding of the ultimate limits of spaceplates is lacking, especially regarding the issue of bandwidth, which remains as a crucial roadblock for the adoption of this platform. In this work, we derive fundamental bounds on the bandwidth of spaceplates as a function of their numerical aperture and compression ratio (ratio by which the freespace pathway is compressed). The general form of these bounds is universal and can be applied and specialized for different broad classes of spacecompression devices, regardless of their particular implementation. Our findings also offer relevant insights into the physical mechanism at the origin of generic spacecompression effects and may guide the design of higher performance spaceplates, opening new opportunities for ultracompact, monolithic, planar optical systems for a variety of applications.
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Limitedsize receiver (Rx) apertures and transmitter–Rx (Tx–Rx) misalignments could induce power loss and modal crosstalk in a modemultiplexed freespace link. We experimentally demonstrate the mitigation of these impairments in a 400 Gbit/s fourdatachannel freespace optical link. To mitigate the above degradations, our approach of singularvaluedecompositionbased (SVDbased) beam orthogonalization includes (1) measuring the transmission matrix
$\text{H}$ for the link given a limitedsize aperture or misalignment; (2) performing SVD on the transmission matrix to find the$\text{U}$ ,$\mathrm{\Sigma <\#comment/>}$ , and$\text{V}$ complex matrices; (3) transmitting each data channel on a beam that is a combination of Laguerre–Gaussian modes with complex weights according to the$\text{V}$ matrix; and (4) applying the$\text{U}$ matrix to the channel demultiplexer at the Rx. Compared with the case of transmitting each channel on a beam using a single mode, our experimental results when transmitting multimode beams show that (a) with a limitedsize aperture, the power loss and crosstalk could be reduced by$\sim <\#comment/>8$ and$\sim <\#comment/>23\phantom{\rule{thickmathspace}{0ex}}\text{dB}$ , respectively; and (b) with misalignment, the power loss and crosstalk could be reduced by$\sim <\#comment/>15$ and$\sim <\#comment/>40\phantom{\rule{thickmathspace}{0ex}}\text{dB}$ , respectively. 
We experimentally demonstrate the utilization of adaptive optics (AO) to mitigate intragroup power coupling among linearly polarized (LP) modes in a gradedindex fewmode fiber (GI FMF). Generally, in this fiber, the coupling between degenerate modes inside a modal group tends to be stronger than between modes belonging to different groups. In our approach, the coupling inside the
${\mathrm{L}\mathrm{P}}_{11}$ group can be represented by a combination of orbitalangularmomentum (OAM) modes, such that reducing power coupling in OAM set tends to indicate the capability to reduce the coupling inside the${\mathrm{L}\mathrm{P}}_{11}$ group. We employ two output OAM modes$l=+1$ and$l=<\#comment/>1$ as resultant linear combinations of degenerate${\mathrm{L}\mathrm{P}}_{11\mathrm{a}}$ and${\mathrm{L}\mathrm{P}}_{11\mathrm{b}}$ modes inside the${\mathrm{L}\mathrm{P}}_{11}$ group of a$\sim <\#comment/>0.6\text{}\mathrm{k}\mathrm{m}$ GI FMF. The power coupling is mitigated by shaping the amplitude and phase of the distorted OAM modes. Each OAM mode carries an independent 20, 40, or 100Gbit/s quadraturephaseshiftkeying data stream. We measure the transmission matrix (TM) in the OAM basis within${\mathrm{L}\mathrm{P}}_{11}$ group, which is a subset of the full LP TMmore » 
We experimentally demonstrate simultaneous turbulence mitigation and channel demultiplexing in a 200 Gbit/s orbitalangularmomentum (OAM) multiplexed link by adaptive wavefront shaping and diffusing (WSD) the light beams. Different realizations of two emulated turbulence strengths (the Fried parameter
${r}_{0}=0.4,\phantom{\rule{thinmathspace}{0ex}}1.0\phantom{\rule{thickmathspace}{0ex}}\mathrm{m}\mathrm{m}$ ) are mitigated. The experimental results show the following. (1) Crosstalk between OAM$l=+1$ and$l=<\#comment/>1$ modes can be reduced by$><\#comment/>10.0$ and$><\#comment/>5.8\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ , respectively, under the weaker turbulence (${r}_{0}=1.0\phantom{\rule{thickmathspace}{0ex}}\mathrm{m}\mathrm{m}$ ); crosstalk is further improved by$><\#comment/>17.7$ and$><\#comment/>19.4\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ , respectively, under most realizations in the stronger turbulence (${r}_{0}=0.4\phantom{\rule{thickmathspace}{0ex}}\mathrm{m}\mathrm{m}$ ). (2) The optical signaltonoise ratio penalties for the bit error rate performance are measured to be$\sim <\#comment/>0.7$ and$\sim <\#comment/>1.6\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ under weaker turbulence, while measured to be$\sim <\#comment/>3.2$ and$\sim <\#comment/>1.8\phantom{\rule{thickmathspace}{0ex}}\mathrm{d}\mathrm{B}$ under stronger turbulence for OAM$l=+1$ and$l=<\#comment/>1$ mode, respectively.